The main goal of the present communication is to test, in terms of computing time cost and precision, Poisson equation solvers in a cubic 3D configuration for further applications in 3D streamer simulation using High Performance Parallel Computing. The Poisson equation is discretized with the Finite Volume Method and the cubic domain is divided into n´n´n nodal points (n being 50, 100 or 200). The chosen configuration could be a basic block of a larger discretized domain distributed on several processors. The upper and the lower planes of the cubic domain are respectively the anode and the cathode, while the other lateral surfaces are open space. The calculation is either performed for the geometric field (Laplace equation) or takes into account the propagation of an analytical space charge density.